Abstract
The Einstein-conformally coupled scalar field system is studied in the presence of a cosmological constant. We consider a massless or massive scalar field with no additional self-interaction, and spherically symmetric black hole geometries. When the cosmological constant is positive, no scalar hair can exist and the only solution is the Schwarzschild–de Sitter black hole. When the cosmological constant is negative, stable scalar field hair exists provided the mass of the scalar field is not too large.
Similar content being viewed by others
REFERENCES
S. Perlmutter et al., “Supernova cosmology project,” Nature 391, 51–54 (1998).
O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Phys. Rep. 323, 184–386 (2000).
A. Strominger, J. High Energy Physics 0110, 034(2001).
L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690–4693 (1999).
J. D. Bekenstein, Phys. Rev. D 5, 1239–1246 (1972).
M. Heusler, Black Hole Uniqueness Theorems (Cambridge University Press, Cambridge, 1996).
J. D. Bekenstein, in Proceedings of the Second International Sakharov Conference on Physics, Moscow, Russia, May 20–23, 1996, I. M. Dremin and A. M. Semikhatov, eds. (World Scientific, Singapore, 1997), pp. 216–219.
J. D. Bekenstein, Phys. Rev. D 5, 2403–2412 (1972).
T. Torii, K. Maeda, and M. Narita, Phys. Rev. D 59, 064027(1999).
R-G. Cai and J-Y. Ji, Phys. Rev. D 58, 024002(1998).
M. S. Volkov and D. V. Gal'tsov, Phys. Rep. 319, 2–83 (1999).
M. Heusler, Class. Quantum Gravity 12, 779–789 (1995).
M. Heusler and N. Straumann, Class. Quantum Gravity 9, 2177–2189 (1992).
D. Sudarsky, Class. Quantum Gravity 12, 579–584 (1995).
J. D. Bekenstein, Phys. Rev. D 51, R6608-R6611 (1995).
T. Torii, K. Maeda, and M. Narita, Phys. Rev. D 64, 044007(2001).
D. Sudarsky and J. A. Gonzalez, “On black hole scalar hair in asymptotically anti de Sitter spacetimes,” preprint gr-qc/0207069 (2002).
E. Winstanley, Class. Quantum Gravity 16, 1963–1978 (1999).
J. D. Bekenstein, Ann. Phys. 82, 535–547 (1974).
J. D. Bekenstein, Ann. Phys. 91, 75–82 (1975).
N. M. Bocharova, K. A. Bronnikov, and V. N. Mel'nikov, Vestnik Moskov. Univ. Fizika 25, 706–709 (1970).
D. Sudarsky and T. Zannias, Phys. Rev. D 58, 087502(1998).
K. A. Bronnikov and Y. N. Kireyev, Phys. Lett. A 67, 95–96 (1978).
B. C. Xanthopoulos and T. Zannias, J. Math. Phys. 32, 1875–1880 (1991).
C. Martinez, R. Troncoso, and J. Zanelli, “De Sitter black hole with a conformally coupled scalar field in four dimensions,” Phys. Rev. D 67, 024008(2003).
A. E. Mayo and J. D. Bekenstein, Phys. Rev. D 54, 5059–5069 (1996).
A. Saa, J. Math. Phys. 37, 2346–2351 (1996).
A. Saa, Phys. Rev. D 53, 7377–7380 (1996).
I. Pe~na and D. Sudarsky, Class. Quantum Gravity 18, 1461–1474 (2001).
K-I. Maeda, Phys. Rev. D 39, 3159–3162 (1989).
P. Kanti, N. E. Mavromatos, J. Rizos, K. Tamvakis, and E. Winstanley, Phys. Rev. D 54, 5049–5058 (1996).
N. E. Mavromatos and E. Winstanley, Phys. Rev. D 53, 3190–3214 (1996).
O. Sarbach and E. Winstanley, Class. Quantum Gravity 18, 2125–2146 (2001).
E. Winstanley and O. Sarbach, Class. Quantum Gravity 19, 689–723 (2002).
P. Breitenlohner and D. Z. Freedman, Phys. Lett. B 115, 197–201 (1982).
P. Breitenlohner and D. Z. Freedman, Ann. Phys. 144, 249–281 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Winstanley, E. On the Existence of Conformally Coupled Scalar Field Hair for Black Holes in (Anti-)de Sitter Space. Foundations of Physics 33, 111–143 (2003). https://doi.org/10.1023/A:1022871809835
Issue Date:
DOI: https://doi.org/10.1023/A:1022871809835